Mathematics

# $\displaystyle \int_{-3\pi}^{3\pi}{\sin^{2}\theta\sin^{2} 2\theta d \theta}$ is equal to-

$\pi$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
If $\int\limits_0^1 {\frac{{\sin t}}{{1 + t}}} dt = \alpha ,\,then\,\int\limits_{4\pi - 2}^{4\pi } {\frac{{\sin (t/2)}}{{4\pi + 2 - t}}dt}$ in terms of $\alpha$ is given by
• A.
• B. $\alpha$
• C. $2 \alpha$
• D. $- \alpha$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int { \cfrac { x }{ 1+{ x }^{ 4 } } } dx$ is equal to
• A. $\cfrac { 1 }{ 2 } \cot ^{ -1 }{ { x }^{ 2 } } +C$
• B. $\cot ^{ -1 }{ { x }^{ 2 } } +C$
• C. $\tan ^{ -1 }{ { x }^{ 2 } } +C\quad$
• D. $\cfrac { 1 }{ 2 } \tan ^{ -1 }{ { x }^{ 2 } } +C\quad$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
A disc, sliding on an inclined plane , is found to have its position (measured from the top of the plane) at any instant given by $x = 3{t^2} + 1$ where $x$ is in meter and $t$ in second. Its average velocity in the time interval between $2s\,to\,2$is
• A. $10.2\,m{s^{ - 1}}$
• B. $15.5\,m{s^{ - 1}}$
• C. $9.7\,m{s^{ - 1}}$
• D. $12.3\,m{s^{ - 1}}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
If $f(x)=\int { \left( \dfrac { x^2+\sin^2x }{ 1+x^2 } \right) } \sec^2 x dx$ and f(0)=0,then  f (1) equals:
• A. $1-\dfrac { \pi }{ 4 }$
• B. $-\dfrac { \pi }{ 4 }$
• C. $\tan 1+1$
• D. $\tan 1-\dfrac { \pi }{ 4 }$

Find $\displaystyle \int_{0}^{\pi/2} \sin x. \sin 2x\ dx$